Cameras operate by converting light reflected from a three dimensional object into a two dimensional image. The conversion between different numbers of dimensions uses a "projection" to transform between the multiple dimensions. Conceptually, camera-type devices, including lens-operated cameras, CCD arrays, and photosensitive elements and the like, all operate in the same way.
FIG. 1 shows an object 100 producing light reflections 101 input to a lens system 110. The angle .theta. of the lens limits the amount of the object 100 which can be seen at one time. This angle .THETA., therefore, defines the maximum amount of the object which can be imaged. Therefore, for lens 110 with angle .theta., the part of the object between area 102 and 104 can be simultaneously imaged. A wider angle lens can image more of the object.
The rays of light are focused by the lens 110 onto an image receiving surface 120, which in a camera is embodied by a photoplate.
The lens can alter the light in various ways for various conditions. A conventional pinhole camera allows a single ray of light from each point on the object to impinge therethrough. Therefore, light from the point A on the object 100 is received at point B on the image receiving surface 120. If the object 100 is at the focal length distance 130 from the lens 110, then the dimension B can be related to the dimension A by any desired transformation amount, where the axis 132 is the central axis of the device. For example, lenses are known wherein B=A; B=sin A, B=Fourier transform (A) and other relations.
The inventors, however, recognized that linear perspective images may become distorted, especially as the angle of the lens increases. For a 180.degree. lens, the photoplate would need to become theoretically infinite. Techniques such as "fisheye lens", described in U.S. Pat. Nos. 4,412,726; 4,647,161; 4,464,029 are used to avoid the necessity for an infinite photoplate.
FIG. 1A shows a direct view transformation of a scene, and FIG. 1B shows a linear perspective view of that scene. Notice how the circles/spheres in FIG. 1A have become distorted in FIG. 1B. The straight lines in FIG. 1B, however, have become curved in FIG. 1A.
It is known that we can apply a conformal or angle-preserving transformation to an image, in a way that preserves the amount of direct view distortion. The curvature distortion can be further reduced by choosing an appropriate conformal transformation T and interpolating between T(DP(r)) and r.
It is an object of the present invention to correct for the geometric perceptual distortion which occurs in such pictures. This is done according to a first aspect of the present invention by transforming the images using a tradeoff between two competing transforms, to maximize the amount of distortion compensation. This can be done either via an optical correction mechanism or by an electronic correction.